Caden had to collect some fruits from two shops and deliver some fruits to another shop. He collected from Shop J and the ratio of apples to oranges was 1 : 2. When he reached Shop K, he unloaded ⁹₁₀ of the oranges and some apples from his van. The ratio of apples to oranges became 3 : 4. At Shop L, 51 apples and 31 oranges were collected and the number of apples to oranges became the same.

1. How many fruits were there on his van after visiting Shop L?
2. How many apples were delivered to Shop K?

	Location	Apples	Oranges
Comparing apples and oranges at first	Shop J	1x20 = 20 u	2x20 = 40 u
Before 1	Shop J	20 u	10x4 = 40 u
Change 1	Shop K	- ?	- 9x4 = - 36 u
After 1	Shop L	3 u	1x4 = 4 u
Before 2	Shop L	3x1 = 3 u	4x1 = 4 u
Change 2	Shop L	+ 51	+ 31
After 2	Shop L	3 u + 51	4 u + 31

(a)
The number of oranges after unloading at Shop K is repeated.  Make the number of oranges left after unloading at Shop K the same.  LCM of 4 and 1 is 4.

The number of oranges collected at Shop J is repeated.  Make the number of oranges collected at Shop J the same by multiplying 2 by 20. 
 
The number of apples and oranges in the end is the same.

4 u + 31 = 3 u + 51
4 u - 3 u = 51 - 31

1 u = 20

Number of apples on his van after collecting from Shop L
= 3 u + 51
= 3 x 20 + 51
= 60 + 51
= 111

Number of fruits on his van after collecting from Shop L
= 2 x 111 
= 222 

(b)
Number of apples delivered to Shop K
= 20 u - 3 u
= 17 u
= 17 x 20
= 340

Answer(s): (a) 222; (b) 340